The paper introduces a model‑free, noise‑aware Bayesian clustering framework that builds a martingale posterior over clusterings without specifying a likelihood or prior, avoiding costly MCMC and variational methods. It handles irregular cluster shapes and allows parallel posterior sampling. To interpret the high‑dimensional posterior, a Wasserstein‑type summarization compresses many draws into a small set of weighted representatives using a novel noise‑aware loss, while marginalising uncertainty in the density level and providing theoretical guarantees.
arXiv:2603.03188v3 Announce Type: replace-cross Abstract: Density-based clustering is a well-established framework that defines clusters through topological or geometric features of the data-generati...
arXiv:2607. 21847v1 Announce Type: cross Abstract: We introduce the distributional determinantal point process (dDPP) as a novel repulsive point process whose atoms are probability distributions rather than points in a real space.
arXiv:2608. 19067v1 Announce Type: cross Abstract: The empirical success of diffusion models in generative modelling has motivated theoretical work, including quantitative error bounds and qualitative analyses that characterise the different phases of denoising.
arXiv:2610.01034v1 Announce Type: cross Abstract: Bayesian inference increasingly uses informative but implicit priors represented only by samples, such as historical ensembles, simulator outputs, an...
The paper introduces a two-way guidance framework that jointly learns summary statistics and posterior distributions for Bayesian simulation-based inference. By imposing a structural restriction on the learned summary, the method ensures that the posterior remains sufficient, while the posterior objective simultaneously steers the summary toward sufficiency. The authors provide theoretical guarantees on posterior estimation error and the deviation of the learned summary from sufficiency, outlining conditions on simulation budgets needed to recover increasingly concentrated posteriors as observation size grows.
arXiv:2410. 14843v4 Announce Type: replace-cross Abstract: Vanilla variational inference finds an optimal approximation to the Bayesian posterior distribution, but even the exact Bayesian posterior is often not meaningful under model misspecification.
arXiv:2512. 04954v3 Announce Type: replace Abstract: We present a novel technique for amortized posterior estimation using Normalizing Flows trained with likelihood-weighted importance sampling.
arXiv:2606. 02453v1 Announce Type: cross Abstract: Despite the remarkable fidelity of generative models, they frequently suffer from mode collapse.
arXiv:2606. 19643v1 Announce Type: cross Abstract: Motivated by the privacy, sensitivity and sharing limitations of health data, we present a comprehensive pipeline for inference of Bayesian mixture models within a federated learning setting, i.
arXiv:2411. 00214v2 Announce Type: replace-cross Abstract: Otto's Wasserstein gradient flow of the inclusive (forward) Kullback--Leibler (KL) divergence offers a principled framework for analyzing statistical inference algorithms, yet algorithms targeting the exclusive (reverse) KL divergence are rarely studied with such tools.
The paper introduces a learning-based approach to replace the MCMC step in split-Gibbs diffusion posterior sampling. By reformulating both Gibbs updates as Gaussian denoising problems, the method uses ODE diffusion for the prior step with a pretrained denoiser and a lightweight deep-unfolded network for the likelihood step. Experiments on nonlinear phase retrieval show that this alternative reduces likelihood-update cost while maintaining effectiveness compared to MCMC-based split Gibbs.
arXiv:2606. 25882v1 Announce Type: new Abstract: DGPs are probabilistic models with remarkable prediction performance that concatenate GPs across several layers.